I use this blog to gather information and thoughts about invention and innovation, the subjects I've been teaching at Stanford University Continuing Studies Program since 2005.
The current course is Principles of Invention and Innovation (Summer '17).
Our book "Scalable Innovation" is now available on Amazon http://www.amazon.com/Scalable-Innovation-Inventors-Entrepreneurs-Professionals/dp/1466590971/

Sunday, January 22, 2012

Counting without numbers.

A paper in Nature Neuroscience shows that a neural network can learn how to count without any knowledge of numbers. Internally, it forms neuron firing patterns that are closer to the set theory than to arithmetic. This research is a step toward an explanation for Approximate Number Sense (ANS), which is present in many animals, including humans (take a simple test to get a feeling for your own ANS).

08 January 2012. Nature Neuroscience (2012). doi:10.1038/nn.2996 ---
Here we show that visual numerosity emerges as a statistical property of images through unsupervised learning. We used deep networks, multilayer neural networks that contain top-down connections and learn to generate sensory data rather than to classify it8, 9. Stochastic hierarchical generative models are appealing because they develop increasingly more complex distributed nonlinear representations of the sensory input across layers9. These features make deep networks particularly attractive for the purpose of neuro-cognitive modeling.

The ability to approximate (estimate), rather than calculate, can be critical in complex situations. It might also explain why invention of number Zero was so controversial. We have a hard time "seeing", i.e. creating an internal neural network representation, a non-existing pattern.